Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 951-969 |
| Seitenumfang | 19 |
| Fachzeitschrift | International Journal of Mathematics |
| Jahrgang | 21 |
| Ausgabenummer | 7 |
| Publikationsstatus | Veröffentlicht - 1 Juli 2010 |
Abstract
In this paper, we introduce the SasakiRicci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a SasakiEinstein metric. Hence it is an odd-dimensional counterpart of the KählerRicci flow. We prove its well-posedness and long-time existence. In the negative or null case the flow converges to the unique η-Einstein metric. In the positive case the convergence remains in general open. The paper can be viewed as an odd-dimensional counterpart of Cao's results on the KählerRicci flow.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: International Journal of Mathematics, Jahrgang 21, Nr. 7, 01.07.2010, S. 951-969.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - The Sasaki-Ricci flow
AU - Smoczyk, Knut
AU - Wang, Guofang
AU - Zhang, Yongbing
N1 - Funding information: This research has been supported in parts by the DFG-Priority Program “Global Methods in Complex Geometry”, SPP 1094.
PY - 2010/7/1
Y1 - 2010/7/1
N2 - In this paper, we introduce the SasakiRicci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a SasakiEinstein metric. Hence it is an odd-dimensional counterpart of the KählerRicci flow. We prove its well-posedness and long-time existence. In the negative or null case the flow converges to the unique η-Einstein metric. In the positive case the convergence remains in general open. The paper can be viewed as an odd-dimensional counterpart of Cao's results on the KählerRicci flow.
AB - In this paper, we introduce the SasakiRicci flow to study the existence of η-Einstein metrics. In the positive case any η-Einstein metric can be homothetically transformed to a SasakiEinstein metric. Hence it is an odd-dimensional counterpart of the KählerRicci flow. We prove its well-posedness and long-time existence. In the negative or null case the flow converges to the unique η-Einstein metric. In the positive case the convergence remains in general open. The paper can be viewed as an odd-dimensional counterpart of Cao's results on the KählerRicci flow.
KW - η-Einstein metric
KW - SasakiEinstein metric
KW - SasakiRicci flow
UR - http://www.scopus.com/inward/record.url?scp=77955185355&partnerID=8YFLogxK
U2 - 10.1142/S0129167X10006331
DO - 10.1142/S0129167X10006331
M3 - Article
AN - SCOPUS:77955185355
VL - 21
SP - 951
EP - 969
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 7
ER -